Updated on 2022/05/21

写真a

 
HAYAKAWA, Yu
 
Affiliation
Faculty of International Research and Education, School of International Liberal Studies
Job title
Professor

Concurrent Post

  • Faculty of Science and Engineering   Graduate School of Fundamental Science and Engineering

Education

  • 1986
    -
    1992

    The University of California at Berkeley   College of Engineering   Operations Research  

    PhD

  • 1983
    -
    1986

    Illinois State University   Department of Mathematics   Mathematics  

    Master of Science

  • 1978
    -
    1983

    Hiroshima University   Faculty of School Education   Elementary School Education  

Degree

  • University of California at Berkeley   Doctor of Philosophy

Research Experience

  • 2007
    -
     

    Professor, Waseda University (1 May Present)

  • 2004
    -
     

    Associate Professor, Waseda University (1 April April 2007)

  • 2001
    -
     

    Senior Lecturer, Victoria University of Wellington, New Zealand (1 January March 2004)

  • 1992
    -
     

    Lecturer, Victoria University of Wellington, New Zealand (1 September December 2000)

Professional Memberships

  •  
     
     

    IEEE

  •  
     
     

    Reliability Engineering Association of Japan

  •  
     
     

    Operations Research Society of Japan

 

Research Areas

  • Others

Research Interests

  • Operations Research

Papers

  • Discussion of “Virtual age, is it real?”

    Richard Arnold, Stefanka Chukova, Yu Hayakawa

    Applied Stochastic Models in Business and Industry    2020  [Refereed]  [Invited]

  • Mean and Variance of an Alternating Geometric Process

    Richard Arnold, Stefanka Chukova, Yu Hayakawa, Sarah Marshall

    2020 Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modeling (APARM)    2020  [Refereed]

    DOI

  • Nonparametric Bayesian Analysis of Hazard Rate Functions using the Gamma Process Prior

    Richard Arnold, Stefanka Chukova, Yu Hayakawa

    2020 Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modeling (APARM)    2020  [Refereed]

    DOI

  • Delayed Reporting of Faults in Warranty Claims

    Richard Arnold, Stefanka Chukova, Yu Hayakawa

    IEEE Transactions on Reliability   69 ( 4 ) 1178 - 1194  2020  [Refereed]

    DOI

  • Nonzero repair times dependent on the failure hazard

    Richard Arnold, Stefanka Chukova, Yu Hayakawa, Sarah Marshall

    Quality and Reliability Engineering International   36 ( 3 ) 988 - 1004  2020  [Refereed]

  • Geometric-Like Processes: An Overview and Some Reliability Applications

    Richard Arnold, Stefanka Chukova, Yu Hayakawa, Sarah Marshall

    Reliability Engineering and System Safety   201   106990  2020  [Refereed]

  • Warranty cost analysis with an alternating geometric process

    Richard Arnold, Stefanka Chukova, Yu Hayakawa, Sarah Marshall

    Journal of Risk and Reliability   233 ( 4 ) 698 - 715  2019  [Refereed]

    DOI

  • Geometric and Geometric-Like Processes and Their Applications in Warranty Analysis

    Richard Arnold, Stefanka Chukova, Yu Hayakawa, Sarah Marshall

    In book: Mathematics Applied to Engineering and Management     1 - 23  2019  [Refereed]  [Invited]

  • Warranty Cost Analysis with an Alternating Geometric Process

    Richard Arnold, Stefanka Chukova, Yu Hayakawa, Sarah Marshall

    Research Report Series, School of Mathematics and Statistics, Victoria University of Wellington   ( #18-1 )  2018

  • Warranty cost analysis: Increasing warranty repair times

    Sarah Marshall, Richard Arnold, Stefanka Chukova, Yu Hayakawa

    Applied Stochastic Models in Business and Industry   34 ( 4 ) 544 - 561  2018  [Refereed]

  • Inference for Multicomponent Systems With Dependent Failures

    Richard Arnold, Stefanka Chukova, Yu Hayakawa

    IEEE Transactions on Reliability   66 ( 3 ) 616 - 629  2017  [Refereed]

    DOI

  • Failure distributions in multicomponent systems with imperfect repairs

    Richard Arnold, Stefanka Chukova, Yu Hayakawa

    Journal of Risk and Reliability   230 ( 1 ) 4 - 17  2016  [Refereed]

    DOI

  • Delayed Reporting of Faults in Warranty Claims

    Richard Arnold, Stefanka Chukova, Yu Hayakawa

    In proceedings: Advanced Reliability and Maintenance Modeling VII: Recent Developments on Reliability, Maintainability and Dependability     9 - 16  2016  [Refereed]

  • Joint modelling of failure times and severities using fuzzy clustering

    Richard Arnold, Stefanka Chukova, Yu Hayakawa, Ivy Liu

    Proceedings of the 6th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modelling (APARM 2014)     1 - 8  2014  [Refereed]

  • Failure distributions in multicomponent systems with imperfect repairs

    Richard Arnold, Stefanka Chukova, Yu Hayakawa

    Proceedings of the 6th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modelling (APARM 2014)     17 - 24  2014  [Refereed]

  • Warranty Cost Analysis: Non-zero Geometric Repair Times

    Richard Arnold, Stefanka Chukova, Yu Hayakawa

    Proceedings of the 6th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modelling (APARM 2014)     9 - 16  2014  [Refereed]

  • Warranty/maintenance: on modelling non-zero rectification times

    Stefanka Chukova, Yu Hayakawa

    In book: Stochastic Reliability and Maintenance Modeling: Essays in Honor of Professor Shunji Osaki on His 70th Birthday     63 - 99  2013  [Invited]

  • Inference for Multicomponent Systems with Dependent Failures

    Richard Arnold, Stefanka Chukova, Yu Hayakawa

    Proceedings of the 5th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modeling (APARM 2012)     9 - 16  2012  [Refereed]

  • On warranty cost analysis: on modelling warranty repairs

    Stefanka Chukova, Yu Hayakawa

    Proceedings of the 7th International Conference on Mathematical Methods in Reliability: Theory, Methods and Applications (MMR 2011)     7 - 13  2011

  • Capture Recapture Estimation Using Finite Mixtures of Arbitrary Dimension

    Richard Arnold, Yu Hayakawa, Paul Yip

    BIOMETRICS   66 ( 2 ) 644 - 655  2010.06  [Refereed]

     View Summary

    Reversible.jump Marko' chain Monte Carlo (RJMCMC) methods are used to fit Bayesian capture recapture models incorporating heterogeneity in individuals and samples. Heterogeneity in capture probabilities comes from finite mixtures and/or fixed sample effects allowing for interactions. Estimation by RJMCMC allows automatic model selection and/or model averaging. Priors on the parameters stabilize the estimates and produce realistic credible intervals for population size for overparameterized models; in contrast to likelihood-based methods. To demonstrate the approach we analyze the standard Snowshoe hare and Cottontail rabbit data sets from ecology, a reliability testing data set.

    DOI

  • Failure model for multicomponent systems with damage accumulation

    Anastasiadis, S, Arnold, R, Chukova, S, Hayakawa, Y

    Advanced Reliability Modeling IV: Beyond the Traditional Reliability and Maintainability Approaches, eds. Chukova, S., Haywood, J. and Dohi, T.     9 - 16  2010  [Refereed]

  • Schur-concavity, aging and a new model for damage accumulation in multi-component systems

    Richard Arnold, Stefanka Chukova, Yu Hayakawa

    Advanced Reliability Modelling III: Global Aspect of Reliability and Maintainability, eds. Sheu, S.-H. and Dohi, T.     627 - 634  2008

  • Optimal two-dimensional warranty repair strategy

    S. Chukova, Y. Hayakawa, M. R. Johnston

    Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability   221 ( 4 ) 265 - 273  2007.12

     View Summary

    For repairable products, the warrantor has options in choosing the type of repair performed to an item that fails within the warranty period. The focus is on a particular warranty repair strategy, related to the degree of the warranty repair, under a non-renewing two-dimensional warranty policy that is free of charge to the consumer. A rectangular warranty region, as in the automotive industry, is considered and partitioned into disjoint subregions. Each of these subregions has a preassigned degree of repair for a faulty item. First, for a partition of size n, an expression is derived for the associated expected warranty servicing cost per item sold. Second, using an example, for a given discretization of the warranty period, the way in which the number of subregions and their shape can be determined, so that the expected warranty servicing cost per item sold is minimum, is demonstrated. © 2007, Institution of Mechanical Engineers. All rights reserved.

    DOI

  • Warranty analysis: Estimation of the degree of imperfect repair via a Bayesian approach

    S. Chukova, Y. Hayakawa, R. Arnold

    RECENT ADVANCES IN STOCHASTIC OPERATIONS RESEARCH     3 - +  2007  [Refereed]

     View Summary

    An approach to modeling imperfect repairs under warranty settings is presented in Chukova, Arnold and Wang(12). They model the imperfect repairs using the concepts of delayed and accelerated distribution functions. As an extension of their approach, we design a procedure for estimating the degree of repair as well as other modeling parameters by Markov chain Monte Carlo (McMC) methods.

  • The effect of Bayesian and frequentist methods on reliability studies

    Stefanka Chukova, Yu Hayakawa

    Proceedings of the 57th Symposium of the Operations Research Society of Japan     19 - 33  2007  [Invited]

  • 信頼性理論の研究におけるベイズ的方法と頻度論的方法の影響

    Stefanka Chukova, 早川 有

    オペレーションズ・リサーチ   52 ( 7 ) 390 - 396  2007

  • A beta-binomial model for estimating the size of a heterogeneous population

    PSF Yip, LQ Xi, R Arnold, Y Hayakawa

    AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS   47 ( 3 ) 299 - 308  2005.09  [Refereed]

     View Summary

    This paper compares the properties of various estimators for a beta-binomial model for estimating the size of a heterogeneous population. It is found that maximum likelihood and conditional maximum likelihood estimators perform well for a large population with a large capture proportion. The jackknife and the sample coverage estimators are biased for low capture probabilities. The performance of the martingale estimator is satisfactory, but it requires full capture histories. The Gibbs sampler and Metropolis-Hastings algorithm provide reasonable posterior estimates for informative priors.

  • Warranty cost analysis: Quasi-renewal inter-repair times

    Stefanka Chukova, Yu Hayakawa

    International Journal of Quality and Reliability Management   22 ( 7 ) 687 - 698  2005

     View Summary

    Purpose - To provide a brief introduction to warranty analysis and a classification of general repairs. To introduce the notion of accelerated probability distribution and use it to model imperfect warranty repairs. Design/methodology/approach - The notion of accelerated probability distribution is discussed and its similarity with quasi-renewal and geometric processes is observed. An approach to modeling imperfect warranty repairs based on the accelerated probability distributions is presented, and the corresponding expected warranty cost over the warranty period under non-renewing free replacement warranty policy is evaluated. Findings - It is observed that quasi-renewal and the geometric processes are equivalent. Using data from an existing warranty database it is shown that the inter-repair times form a quasi-renewal process. The corresponding expected warranty cost over the warranty period under a non-renewing free replacement warranty policy is evaluated. Research limitations/implications - This approach is applicable only if the cost of the warranty repair is an increasing function of the number of repairs. Practical implications - Provides a useful approach to modeling inter-repair times incorporating the idea of imperfect repairs in practice. Originality/value - Provides an approach to model imperfect warranty repairs and to evaluate the corresponding expected warranty cost. © Emerald Group Publishing Limited.

    DOI

  • Warranty cost analysis: Renewing warranty with non-zero repair time

    Stefanka Chukova, Yu Hayakawa

    International Journal of Reliability, Quality and Safety Engineering   11 ( 2 ) 93 - 112  2004.06

     View Summary

    The main focus of this study is on the modeling of the warranty claims and evaluating the warranty expenses. The cost of each warranty claim depends on the repair time associated with the claim. Alternating renewal process is used to model the operating and repair times. The warranty costs over the warranty period under renewing free replacement policy are evaluated. Also, the expected warranty expenses over the life cycle of the product are studied. Numerical examples illustrate the ideas.

    DOI

  • Warranty and imperfect repairs

    S Chukova, Y Hayakawa

    Advanced Reliability Modeling     81 - 88  2004  [Refereed]

     View Summary

    A brief introduction to concepts and problems in warranty analysis is presented. The degree of warranty repair over the warranty period have an impact on the expected warranty costs and influences consumers' expenses over the post-warranty usage period of the product. Some techniques and approaches for modeling imperfect repairs are reviewed. A particular model is used to illustrate the impact of the degree of repair on warranty servicing costs.

  • Warranty cost analysis: non-renewing warranty with repair time

    S Chukova, Y Hayakawa

    APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY   20 ( 1 ) 59 - 71  2004.01  [Refereed]

     View Summary

    The main focus of this study is on the modelling of the warranty claims and evaluating the warranty expenses. The cost of each warranty claim depends on the non-zero length of the repair time. Alternating renewal process is employed to model the operating and repair times. New results for alternating renewal process in finite horizon are derived. They are used to evaluate the warranty costs over the warranty period under non-renewing free replacement policy and over the life cycle of the product. Examples are provided to illustrate the ideas. Copyright (C) 2004 John Wiley Sons, Ltd.

    DOI

  • Bayesian inference for a stochastic epidemic model with uncertain numbers of susceptibles of several types

    Y Hayakawa, PD O'Neill, D Upton, PSF Yip

    AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS   45 ( 4 ) 491 - 502  2003.12  [Refereed]

     View Summary

    A stochastic epidemic model with several kinds of susceptible is used to analyse temporal disease outbreak data from a Bayesian perspective. Prior distributions are used to model uncertainty in the actual numbers of susceptibles initially present. The posterior distribution of the parameters of the model is explored via Markov chain Monte Carlo methods. The methods are illustrated using two datasets, and the results are compared where possible to results obtained by previous analyses.

  • A frailty model for detecting number of faults in a system

    Y Wang, PSF Yip, Y Hayakawa

    STATISTICA SINICA   12 ( 4 ) 1001 - 1013  2002.10  [Refereed]

     View Summary

    A frailty model for failure data is proposed to estimate the total number of faults in a system. The Littlewood model and Jelinski-Moranda are the two particular cases of the proposed formulation. The two-stage estimating procedure, a conditional likelihood and a Horvitz-Thompson estimator, is found to be efficient. Simulation studies are given to assess the performance of the estimator. Two examples axe also presented.

  • Bayesian Nonparametric Testing of Constant versus Nondecreasing Hazard Rates

    Hayakawa, Y, Zukerman, J, Paul, S, Vignaux, G.A

    In book: System and Bayesian Reliability: Essays in Honor of Professor Richard E. Barlow for his 70th Birthday     391 - 406  2001

    DOI

  • Characterizing failure duration in 2-terminal network problems

    Smith, P.J, Silby, H.W, Hayakawa, Y, Carlisle, C

    International Journal of Reliability, Quality and Safety Engineering   8 ( 2 ) 137 - 158  2001  [Refereed]

  • Bayesian Nonparametric Testing of Constant versus Nondecreasing Hazard Rates, Chapter 23 in "System and Bayesian Reliability: Essays in Honor of Professor Richard E. Barlow for his 70th Birthday"

    Hayakawa, Y, Zukerman, J, Paul, S, Vignaux, G.A

    World Scientific Publishing    2001

  • A Gibbs-sampler approach to estimate the number of faults in a system using capture-recapture sampling

    Y Hayakawa, PSF Yip

    IEEE TRANSACTIONS ON RELIABILITY   49 ( 4 ) 342 - 350  2000.12  [Refereed]

     View Summary

    A new recapture debugging model is suggested to estimate the number of faults in a system, nu, and the failure intensity of each fault, phi. The Gibbs sampler and the Metropolis algorithm are used in this inference procedure. A numerical illustration suggests a notable improvement on the estimation of nu and phi compared with that of a removal debugging model.

  • Mixed Poisson-type processes with application in software reliability

    Y Hayakawa, G Telfar

    MATHEMATICAL AND COMPUTER MODELLING   31 ( 10-12 ) 151 - 156  2000.05  [Refereed]

     View Summary

    We introduce one generalization of the mixed Poisson process referred to as the mixed Poisson-type process. An approach taken here is to assume the l(1)-isotropy of interevent times and to define the parameter as a function of observable quantities. An inhomogeneous variant of the new process is studied as a software reliability model. As an illustration a numerical example is analyzed via the Gibbs sampler. The mixed Poisson-type process is constructed through probabilistic behaviour of observable quantities and includes the mixed Poisson processes the limiting case. (C) 2000 Elsevier Science Ltd. All rights reserved.

  • A new characterisation property of mixed poisson processes via Berman's theorem

    Y Hayakawa

    JOURNAL OF APPLIED PROBABILITY   37 ( 1 ) 261 - 268  2000.03  [Refereed]

     View Summary

    In the literature on mixed Poisson processes, a number of characterisation properties have been studied. As a new characterisation property for mixed Poisson processes, we show that normalised event occurrence times are the order statistics of independent uniform random variables on (0, 1). Berman's theorem on l(p)-isotropic sequences is applied to prove the results.

  • When a large earthquake occurs, what can we say about the aftershocks? A real-life use of probability forecasts (translation from the Japanese)

    Vere-Jones, D, Vere-Jones, M, Hayakawa, Y

    School of Mathematical and Computing Sciences, Victoria University of Wellington, Wellington, New Zealand   ( 6 )  2000

  • The total time on test statistics and l1-isotropy

    Yu Hayakawa

    International Journal of Reliability, Quality and Safety Engineering   7 ( 2 ) 143 - 151  2000  [Refereed]

    DOI

  • Sensitivity-analysis and estimating number-of-faults in removal debugging

    PSF Yip, LQ Xi, DYT Fong, Y Hayakawa

    IEEE TRANSACTIONS ON RELIABILITY   48 ( 3 ) 300 - 305  1999.09  [Refereed]

     View Summary

    Estimating the number of faults in a computer program is important in software debugging. A martingale equation is used to estimate the number of faults in removal-debugging by assuming a known proportionality constant between the failure rate of a 'newly detected fault' and a 'seeded fault'. The sensitivity of the assumption is examined, and the results are generalized to allow an unknown proportionality. The information of the proportionality is shown to be crucial in the precision & availability of the estimates. It is advisable to obtain the information about the proportionality constant from external sources in order to improve the efficiency of the method in this paper.

  • Characterisation properties of mixtures of exponential distributions

    Yu Hayakawa

    Proceedings of the First Western Pacific and Third Australia-Japan Workshop on Stochastic Models in Engineering, Technology and Management     127 - 136  1999

  • A Bayesian positive dependence of survival times based on the multivariate arrangement increasing property

    Y Hayakawa

    JOURNAL OF STATISTICAL PLANNING AND INFERENCE   70 ( 2 ) 225 - 240  1998.07  [Refereed]

     View Summary

    We introduce a new notion of positive dependence of survival times of system components using the multivariate arrangement increasing property. Following the spirit of Barlow and Mendel (J. Amer. Statist. Assoc. 87, 1116-1122), who introduced a new univariate aging notion relative to exchangeable populations of components, we characterize a multivariate positive dependence with respect to exchangeable multicomponent systems. Closure properties of such a class of distributions under some reliability operations are discussed. For an infinite population of systems our definition of multivariate positive dependence can be considered in the frequentist's paradigm as multivariate totally positive of order 2 with an independence condition. de Finetti(-type) representations for a particular class of survival functions are also given. (C) 1998 Elsevier Science B.V. All rights reserved.

  • Bayesian classification of satellite imagery with spatio-temporal dependence applied to low cloud detection

    Hayakawa, Y, Houston, G, Hume, T

    School of Mathematical and Computing Sciences, Victoria University of Wellington, Wellington, New Zealand   ( 45 )  1997

  • THE CONSTRUCTION OF NEW BIVARIATE EXPONENTIAL-DISTRIBUTIONS FROM A BAYESIAN PERSPECTIVE

    Y HAYAKAWA

    JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION   89 ( 427 ) 1044 - 1049  1994.09  [Refereed]

     View Summary

    We use an economic approach of Mendel to derive new bivariate exponential lifetime distributions. Features distinguishing this approach from the existing ones are (1) it makes use of the principle of indifference; (2) our parameter of interest is a measurable function of observable quantities; (3) the assessment of the probability measure for random lifetimes is performed by assessing that for random lifetime costs with a change of variables; and (4) characterization properties other than the bivariate loss-of-memory property are used to construct distributions. For the infinite population case, our distributions correspond to mixtures of existing bivariate exponential distributions such as the Freund distribution, the Marshall-Olkin distribution, and the Friday-Patil distribution. Moreover, a family of natural conjugate priors for Bayesian Freund(-type) bivariate exponential distributions is discussed.

  • Operational Bayesian models for designed experiments

    Yu Hayakawa

    Institute of Statistics and Operations Research, Victoria University of Wellington, Wellington, New Zealand   ( 36 )  1994

  • Derivation of conjugate priors for continuous exponential-type families and l1-isotropic models with right censorship

    Yu Hayakawa

    Proceedings of the 29th Annual Conference of the Operational Research Society of New Zealand     334 - 341  1993

  • Interrelationships between lp-isotropic densities and lp-isotropic survival functions, and de Finetti representations of Schur-concave survival functions

    Yu Hayakawa

    Australian Journal of Statistics   35 ( 3 ) 327 - 332  1993  [Refereed]

    DOI

  • Bayesian Parametric Models for Lifetimes from a Subjectivistic Viewpoint: Model Construction and Characterizations of Aging

    Yu Hayakawa

    Department of Industrial Engineering and Operations Research, University of California at Berkeley, California, U.S.A.    1992

▼display all

Research Projects

  • Non-parametric Bayesian approach to modelling system reliability

    Project Year :

    2018.04
    -
    2021.03
     

  • Non-parametric Bayesian approach to modelling system reliability

    Japan Society for the Promotion of Science  Grants-in-Aids for Scientific Research

    Project Year :

    2018.04
    -
    2020.03
     

  • New models for failures in multi-component systems: Model properties and simulation methods

    Japan Society for the Promotion of Science  Invitational Fellowships for Research in Japan

    Project Year :

    2013.11
    -
    2014.02
     

  • Robustness measures for telecomunication networks

    New Zealand Telecom 

    Project Year :

    1993
    -
    1994
     

     View Summary

    jointly with Peter J Smith

Presentations

  • Schur-concavity, aging and a new model for damage accumulation in multi-component systems (Arnold, R., Chukova, S. and Hayakawa, Y.)

    3rd Asian International Workshop on Advanced Reliability Modeling (AIWARM 2008) 

    Presentation date: 2008.10

  • Capture Recapture estimation using finite mixtures of arbitrary dimension (Arnold, R. and Hayakawa, Y.) presented by Arnold, R.

    9th World Conference of the International Society for Bayesian Analysis (ISBA) 

    Presentation date: 2008.07

Specific Research

  • Non-parametric Bayesian approach to modelling system reliability

    2018   Richard Arnold, Stefanka Chukova, Sarah Marshall

     View Summary

    Weare taking a nonparametric Bayesian approach to hazard function modelling. Thehigh level of complexity of this approach has meant we spent a significantamount of time on review of the literature and on model formulation.  We have created a draft technical reportsummarising our findings and have implanted simulation models for the GammaProcess methodology which we are using. We are also working on biclustering incapture-recapture experiments from a nonparametric Bayesian perspective and arepresenting our results at MMR 2019.  Wewrote a paper on delayed reporting of faults in warranty claims, in which thereporting process is modelled as a stochastic process dependent on theunderlying stochastic process generating the faults.  Our paper has been presented at seminars andconferences. This research inspired another project on nonzero repair timesdependent on the failure hazard.  Ourpaper on this project will be presented at MMR 2019. Wealso worked on a review paper and a book chapter on geometric-like processesand their applications in warranty analysis. Conference and workshop presentations have been given on this topic andwe also present our paper at MMR 2019. The book chapter has been accepted for publication.

  • Warranty cost analysis with non-zero repair times through hierarchical stochastic processes

    2017   Richard Arnold, Stefanka Chukova, Yuuki Rikimaru

     View Summary

    1)    We model the warranty claims process and evaluate the warranty servicing costs under non-renewing and renewing free repair warranties.  We assume that the repair time for rectifying the claims is non-zero and the repair cost is a function of the length of the repair time.  To accommodate the ageing of the product and repair equipment, we use a decreasing geometric process to model the consecutive operational times and an increasing geometric process to model the consecutive repair times.  We identify and study the alternating geometric process (AGP), which is an alternating process with cycles consisting of the item’s operational time followed by the corresponding repair time.  We derive new results for the AGP in finite horizon and use them to evaluate the warranty costs over the warranty period and over the life cycle of the product under a non-renewing free repair warranty (NRFRW), a renewing free repair warranty (RFRW) and a restricted renewing free repair warranty (RRFRW(n)).  Properties of the model are demonstrated using a simulation study.Together with Dr Sarah Marshall, Auckland University of Technology, we wrote a paper on the results of this project and it was made a technical report (Research Report Series (ISSN:1174-2011), #18-1, Victoria University of Wellington School of Mathematics and Statistics (http://sms.victoria.ac.nz/Main/ResearchReportSeries) (2018)).  We submitted this paper to a joint conference: APARM2018 & QR2MSE2018.  We will present this paper at this conference in August 2018.2)    We present a model for the delayed reporting of faults: multiple non-fatal faults are accumulated and then simultaneously reported and repaired.  The reporting process is modelled as a stochastic process dependent on the underlying stochastic process generating the faults.  We have worked on the cases of multiple faults types, planned preventative maintenance and customer rush.  A manuscript has been written on the results and we plan to extend it by adding simulation studies and submit it to an international peer reviewed journal this year.

  • Delayed reporting of faults in warranty claims

    2017   Richard Arnold, Stefanka Chukova

     View Summary

    When a complex system is operated, it may experience multiple faults. If the system is operating under warranty these faults may be claimed for and repaired at zero or minimal cost to the consumer.  However, if the faults do not lead to system failure the user may find it inconvenient to claim for each repair as it occurs and may instead delay making a report or claim until a sufficiently large number of faults has accumulated. We present a model for the delayed reporting of faults: multiple non-fatal faults are accumulated and then simultaneously reported and repaired. The reporting process is modelled as a stochastic process dependent on the underlying stochastic process generating the faults. The joint distribution of the reporting times and numbers of reported faults is derived.  We presented a paper on the project in the 10th International Conference on Mathematical Methods in Reliability held in France on 3-6 July 2017.  We also worked on a few extensions of the above model, which deal with multiple fault types, planned preventative maintenance and customer rush and wrote a manuscript on the results.  We have written a manuscript on the above results and plan to extend it by adding simulation results.  An extended version of the manuscript will be submitted to an international peer review journal later this year.

  • Modelling system reliability: Non-parametric Bayesian inference

    2016   Richard Arnold, Stefanka Chukova, Adam Rod

     View Summary

    1) We construct a model for the delayed reporting of non-fatal faults which are accumulated before being reported in groups, which is applicable to warranty claim analysis. We extend this model to account for multiple fault types, planned preventative maintenance and customer rush. We have submitted a manuscript for presentation in an invited session at the 10th International Conference on Mathematical Methods in Reliability in Grenoble, France, on 3-6 July 2017. We also presented our paper at 2016 Joint NZSA+ORSNZ Conference (27-30 November 2016) and the Joint Workshop – New Development of Stochastic Models (15 October 2016). Our paper on this model was awarded a Best Paper award at the Asia-Pacific Workshop on Advanced Reliability and Maintenance Modelling (Seoul, August 2016).2) We present a general approach to inference in multicomponent systems where the system is viewed as being made up of Independent Overlapping Subsystems (IOS). We submitted a paper on this project to IEEE Transactions on Reliability in February 2016 and submitted a revision of the paper in December 2016.3) We present a unified model for multi-component systems with dependent failures and imperfect repairs. A paper on this project was finalised and submitted to “Stochastic Operations Research in Business and Industry,” World Scientific, for inclusion as a book chapter in December 2016.

  • Stochastic process approaches to modelling system reliability

    2015   Richard Arnold, Stefanka Chukova, Fan Wang

     View Summary

    1) We present a model for the delayed reporting of faults: multiple sub-critical faults are accumulated and then simultaneously reported and repaired. The reporting process is modelled as a stochastic process dependent on the underlying stochastic process generating the faults. The joint distribution of the reporting times and numbers of reported faults is derived.  We have submitted a manuscript for presentation at The 7th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modeling in Seoul, Korea, on 24-26 August 2016.2) We generalise existing approaches to inference in multicomponent systems by formulating the likelihood for systems made up of independent overlapping subsystems, and have shown how to apply this inference procedure to the models that we had previously published.   A paper on this project was finalised and submitted to IEEE Transaction on Reliability in February 2016.3) We model the warranty servicing costs by assuming non-zero increasing repair times.  We introduce the generalised alternating renewal process by using the geometric process.  Simulation is used to estimate the expected costs over the warranty period and life cycle.  We have written a manuscript summarising our results and plan to submit its finalised version to European Journal of Operational Research by August 2016.

  • Generalised alternating renewal process: Bayesian statistical inference with applications

    2014  

     View Summary

    A summaryof research outcomes: Research team of Waseda University Grantfor Special Research Projects (2014B-443) consisted of the following members: Principal researcher: Dr Yu Hayakawa,Waseda UniversityResearch collaborator: Dr Richard Arnold,Victoria University of WellingtonResearch collaborator: Dr Stefanka Chukova,Victoria University of WellingtonResearch collaborator: Ms Ting Ying Chen,Waseda University (undergraduate and masters student) In our research plan submitted for thisgrant, we stated that the main focus is on the modeling of the warranty costsbased on the generalised alternating renewal (GAR) process of type 1 (renewaloperating times followed by geometric repair times) and the GAR of type 2(geometric operating times followed by geometric repair times) under both thenon-renewing and renewing free replacement policies. We also obtain numericalresults by employing simulation methods.  We report that we have made good progresson this project and on some related projects as well. Dr Richard Arnold attended the 6th Asia-Pacific InternationalSymposium on Advanced Reliability and Maintenance Modelling held in Sapporoand visited the School of International Liberal Studies (SILS), WasedaUniversity in August 2014.  Yu Hayakawavisited Victoria University of Wellington from 23 February 2015 to 11 March2015, with which both Drs Richard Arnold and Stefanka Chukova are affiliated.  Throughout the period of this grant, we workedtogether on the project described above and a few other related topicsdescribed below.  We also worked on theproject with Dr Sarah Marshall, Auckland University of Technology, who joinedthe team in December 2014. 1)   We model the warranty claimsprocess and evaluate the warranty servicing costs under non-renewing andrenewing free replacement warranties.  Westudy two models which are based on the generalised alternating renewal processof type 1 (renewal operating times followed by geometric repair times – GAR I)and that of type 2 (geometric operating times followed by geometric repairtimes – GAR II) under both the non-renewing and renewing free replacementpolicies. We derive new results on GAR I & II with a finite time horizon.   Some results are in the manuscripts [1] & [5].  The manuscript [1] was presented by YuHayakawa at the 6th Asia-Pacific International Symposium on AdvancedReliability and Maintenance Modelling (APARM 2014, August 2014, Sapporo, Japan).  The manuscript [5] will be presented by YuHayakawa at The Ninth InternationalConference on Mathematical Methods in Reliability (MMR 2015) in Tokyo on 1-4June 2015. Dr Stefanka Chukova delivered an invited talk on this project atthe  International Statistical InstituteRegional Statistics Conference 2014 (ISI-RSC 2014) held in Kuala Lumpur,Malaysia, on 16-20 November 2014.  Thetalk title was "Warranty cost analysis: geometric operational and repairtimes." Dr Sarah Marshall will present some results on this project at the 27thEuropean Conference on Operational Research held in Glasgow, United Kingdom, 12-15thJuly 2015.  The talk title will be “Modellingwarranty costs using geometric repair times.” Ms Ting Ying Chen created some graphs to summarise simulationresults for this project. We are working on extended versions of the manuscripts [1] & [5]by incorporating the simulation results under both non-renewing and renewingwarranty replacement policies using GAR I and GAR II.  Also we are working on a numerical procedurerelated to some results included in the manuscript [1].   2)   We have constructed a model forcorrelated failures in multicomponent systems where failed components arerepaired.  Our results are in themanuscript [2].  This manuscript waspresented by Dr Richard Arnold at the 6th Asia-Pacific InternationalSymposium on Advanced Reliability and Maintenance Modelling (APARM 2014) inAugust 2014.  An expanded version of thepaper has been accepted for publication in the Journal of Risk and Reliability[4]. 3)   We apply finite mixture methodsto group units into fuzzy clusters, in order to model the joint distribution offailure times and severities.  This workis in the manuscript [3].  Thismanuscript was presented by Dr Richard Arnold at the 6thAsia-Pacific International Symposium on Advanced Reliability and MaintenanceModelling (APARM 2014) in August 2014. 4)   We develop inference proceduresfor multicomponent systems where the system is viewed as being made up ofindependent overlapping subsystems that we had previously published. Weintroduce a new type of grouping of subunits which allow for common causefailures, i.e., all the components within a subunit failuresimultaneously.  We extend our resultsand a paper on this project [6] is close to completion.  

  • Warranty Cost Analysis with Non-zero Repair Times: Models and Inference

    2013  

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    A summary of research outcomes:Research team of Waseda University Grant for Special Research Projects (2013B-246) consisted of the following members:Principal researcher: Dr Yu Hayakawa, Waseda UniversityResearch collaborator: Dr Stefanka Chukova, Victoria University of WellingtonResearch collaborator: Yimo Xu, Waseda University (undergraduate student)Research assistant: Yan Liu, Waseda University (PhD student)In our research plan submitted for this grant, we stated that the main focus is on the modeling of the warranty claims and evaluation of the warranty servicing costs under non-renewing free replacement warranty policy. Our model is based the generalised alternating renewal process and we derive new results on this stochastic process with a finite time horizon. We also employ simulation methods to obtain numerical results. We report that we have made good progress on this project and on some related projects as well.Dr Stefanka Chukova visited the School of International Liberal Studies (SILS), Waseda University, during 12-19 December 2013. Dr Richard Arnold, her colleague from Victoria University of Wellington, was also visiting SILS on sabbatical from November 2013 to February 2014. Throughout the period of this grant, we worked together on the project described above and a few other related topics described below.1) We model the warranty claims process and evaluate the warranty servicing costs under non-renewing and renewing free replacement warranties. We use an increasing geometric process to model the consecutive repair times. This model is based on the generalised alternating renewal process (GAR) and we derive new results on GAR process with a finite time horizon. This work is in the manuscript [1] whose details are given in the next section. This manuscript will be presented at the 6th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modelling (APARM 2014, August 2014, Sapporo, Japan).Yan Liu conducted a simulation study on the above model under non-renewing replacement warranty and obtained numerical results. Yimo Xu wrote a set of notes on the relevant technical details and proofs of the theorems. We are working on an extended version of the manuscript [1] by incorporating the simulation results under both non-renewing and renewing warranty replacement policies (the manuscript [5]).2) We have constructed a model for correlated failures in multicomponent systems where failed components are repaired. Due to these repairs multiple failures of each component are observable. We assume that repair is instantaneous, but imperfect. Correlation amongst failures and the overall ageing of the system are modeled by treating each component failure as a shock which damages the other components in the system. Our results are in the manuscript [2]. This manuscript will be presented at the 6th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modelling (APARM 2014).3) Reliability data may incorporate a failure severity measure as well as the time of each failure. Such severities may however be qualitative ordinal data. We apply finite mixture methods to group units into fuzzy clusters, in order to model the joint distribution of failure times and severities. This work is in the manuscript [3]. This manuscript will be presented at the 6th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modelling (APARM 2014).4) We develop inference procedures for the shock models that we had previously published. We introduce a new type of grouping of subunits which allow for common cause failures, i.e., all the components within a subunit failure simultaneously. A paper on this project is in preparation.

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Overseas Activities

  • Modelling system reliability via stochastic process

    2016.09
    -
    2017.03

    New Zealand   Victoria University of Wellington

  • Studies on damage accumulation models

    2011.09
    -
    2012.03

    ニュージーランド   Victoria University of Wellington

 

Syllabus

 

Committee Memberships

  • 2020.06
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    Reliability Engineering Association of Japan  Vice-president

  • 2015.01
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    2016.12

    IEEE Reliability Society Japan Joint Chapter  Chair